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Level Lowering Modulo Prime Powers and Twisted Fermat Equations

  Published:2011-09-15
 Printed: Apr 2012
  • Sander R. Dahmen,
    Department of Mathematics, The University of British Columbia, Vancouver, BC, V6T 1Z2
  • Soroosh Yazdani,
    Department of Mathematics and Statistics, McMaster University, West Hamilton, ON, L8S 4K1
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Abstract

We discuss a clean level lowering theorem modulo prime powers for weight $2$ cusp forms. Furthermore, we illustrate how this can be used to completely solve certain twisted Fermat equations $ax^n+by^n+cz^n=0$.
Keywords: modular forms, level lowering, Diophantine equations modular forms, level lowering, Diophantine equations
MSC Classifications: 11D41, 11F33, 11F11, 11F80, 11G05 show english descriptions Higher degree equations; Fermat's equation
Congruences for modular and $p$-adic modular forms [See also 14G20, 22E50]
Holomorphic modular forms of integral weight
Galois representations
Elliptic curves over global fields [See also 14H52]
11D41 - Higher degree equations; Fermat's equation
11F33 - Congruences for modular and $p$-adic modular forms [See also 14G20, 22E50]
11F11 - Holomorphic modular forms of integral weight
11F80 - Galois representations
11G05 - Elliptic curves over global fields [See also 14H52]
 

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